Not sure about Handbrake never tried it. I use DVDFAB to rip the movies to mkv and avi and they come out just fine no skips or anything.

The issues you may have could be related to the hardware you are using. If the you are doing stuff while you are encoding and your hardware is not up to the task you can very well get the issues that you are stating. When I was running a low end machine with just 2gbs of ram I would get issues like you are. With my 3.0ghz core2 and 4gbs of ram everything runs smooth now but I still don't do much if any multitasking when encoding. I walk away from the comp and let it encode on its own.

Edited....
Just looked at the specs for Handbrake and it doesn't decrypt the video so you do need AnyDvd to do that for you.
......